This invention relates to seismic exploration and more particulary, to a method for correctly interpolating seismic traces that are spatially aliased.
Seismograms are commonly recorded as digital samples representing the amplitude of a received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formations. Before an array of seismic samples can be converted into a seismic section which can be interpreted by the geophysicist, the array must be extensively processed to remove noise and to make reflection events discernable.
One of the problems which is encountered, is that the recorded seismic traces may exhibit aliasing. Aliasing is caused by coarse sampling. If the seismic signals are not sampled sufficiently frequently, time aliasing is present and seismic signals will not contain the entire seismic frequency band. This is generally not a problem because proper sampling techniques and anti-aliasing filters can be used to prevent time domain aliasing. However, aliasing in the distance domain is not so easily prevented. Uniform sampling may be difficult to obtain in some marine and land surveys. Wind and water currents, physical obstacles, etc., cause abnormal shooting and recording geometries, resulting in irregularly spaced traces and gaps in coverage. Even in uniformly spaced data, the gathering of oblique lines required for interpretation for well ties may result in a large trace spacing, depending on the angle of the line in the survey grid.
Numerous seismic processes are critically dependent upon proper spatial sampling. Migration and velocity techniques are examples of processes which cannot be performed satisfactorily if spatial aliasing is a serious problem.
Spatial aliasing may be present when an insufficient number of seismic traces have been recorded along the line of exploration. Spatial aliasing is compensated for by interpolating between the seismic traces and inserting the interpolated trace into the seismic section. However, trace interpolation is much more difficult than it first appears. To properly interpolate between two seismic traces, it is necessary to find the mean or average amplitude at each increment of time. Even if this is done, there is no assurance that the interpolated trace has values which are within the frequency pass band of the recorded seismic traces.
It is an object of the present invention to provide a technique of quickly and correctly interpolating seismic traces which can be inserted into a seismic section to suppress spatial aliasing.
In the processing of seismograms, x-t arrays have been transformed into arrays representing amplitude as a function of frequency and wave number. This is commonly referred to as an "f-k" transformation. The f-k transformation has been used as a tool to study seismic filtering. U.S Pat. Nos. 3,284,763--Burg et al, and 3,274,541--Embree describe velocity filtering which is carried out in the time domain on digital seismograms. These patents describe a type of velocity filtering which is commonly referred to as "pie slice" because of the shape of the filtered region in the f-k transform of the seismic section. Embree and Burg, et al do not perform a filtering operation on the f-k section; all filtering is in the time domain on sections in the normal x-t arrays U.S. Pat. No. 3,550,073--Foster, et al is an improvement on "pie slice" filtering.
In U.S. Pat. No. 4,218,765--Kinkade, the seismic traces are transformed to f-k array and filtering is performed on the traces while they are in the f-k domain.
It is another object of the present invention to use f-k filtering techniques to interpolate seismic traces so that interpolated traces can be inserted into the seismic section to overcome spatial aliasing.